Question: What do the following two equations represent? $3x+3y = 3$ $-3x-3y = 1$
Putting the first equation in $y = mx + b$ form gives: $3x+3y = 3$ $3y = -3x+3$ $y = -1x + 1$ Putting the second equation in $y = mx + b$ form gives: $-3x-3y = 1$ $-3y = 3x+1$ $y = -1x - \dfrac{1}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.